Congrats, Firebird! Pics please
Don't worry about the battery. Amaron makes good batteries, and your amp is not going to strain the battery any.
Still, it would be a good idea to switch off your system before you turn the engine off, so the system does not add to the load on the battery while starting. This is not such a big deal, but it is a nice habit to get into.
And if you use the ICE on battery power (with the engine off), the battery will drain quite fast.